Übungsblatt Sommerkurs Statistik
Aufgabe 1
Suppose a die is tossed six times. What is the probability of getting exactly three fours?
Aufgabe 2
An insurance company believes that people can be divided into two classes: those who are accident prone and those who are not. The company’s statistics show that an accident-prone person will have an accident at some time within a fixed 1-year period with probability 0.4, whereas this probability decreases to 0.2 for a person who is not accident prone. If we assume that 30 percent of the population is accident prone, what is the probability that a new policyholder will have an accident within a year of purchasing a policy? Suppose that a new policyholder has an accident within a year of purchasing a policy. What is the probability that he or she is accident prone?
Aufgabe 3
A musician is planning to bring out a new album and has recorded eight songs but she is contemplating about the order in which the songs should be arranged on the CD. If the total playing time for the album is 45 minutes, how long will it take her to listen to all the possible arrangements of the eight songs?
Aufgabe 4
An insurance sales representative sells policies to 5 men, all of identical age and in good health. According to the actuarial tables, the probability that a man of this particular age will still be alive in 30 years is \(\frac{2}{3}\). Find the probability that in 30 years exactly 4 men will be alive.
Aufgabe 5
At a hardware store, 4 out of 17 screwdrivers are of inferior quality. You purchase two screwdrivers from that store. Find the probability for one defective screwdriver. Solve the problem
- Using the formula for the hypergeometric distribution
- Using a tree diagram
Aufgabe 6
The time required to assemble an electronic device is normally distributed with a mean of 12 minutes and a standard deviation of 1.5 minutes. Find the probability (using the z-table) that a particular assembly takes…
- less than 14 minutes
- more than 8 minutes